1. Solve 2

Same as other one. How would I solve derivative simplifying results?

g(x)=√2x^4+x^2+1

r(x) 2x^2-5x^-12/x-4

m(x) = -5(x^4+3)^8

k(x)=2x/x^2+2

2. For g(x), I'm taking that to be $\sqrt{2x^4+x^2+1}$ Let u = $2x^4+x^2+1$ and let $\frac{du}{dx}=8x^3+2x$ So g(x) can now be written as $\sqrt{u}$ Now taking the derivative, you get $g'(x)=\frac{1}{2\sqrt{u}}*\frac{du}{dx}$. Now back substitute everything in. Does this method make sense? It can be a lot to take in.

For r(x) and k(x), just use the quotient rule.

$\frac{d}{dx}\frac{u}{v}=\frac{vu'-uv'}{v^2}$

All of the questions use the powerful CHAIN RULE. Make sure to learn that solidly.